Fixed Point Theory is developed during the years by generalizing various types of contractions or changing the axioms of metric spaces. The S-metric spaces extend the concept of metric spaces since the determination of axioms of S-metric are more general. In this paper, we prove a common fixed-point theorem of two mappings in S-metric space. The theorem uses an implicit contractive condition, based on functions of class F6.  With the change of the form of the functions of class F6 , we obtain different results for common fixed points of two functions.

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In this paper we have define and treat (i-s) semi-inner product, which is a generalization of superior semi-inner product function and inferior semi-inner product function.

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